The identification of lacoperon is essentially identified by an in vivo assay. The mutants were created in vivo and selected by the right phenotype. With the invention of recombinant DNA technology, it is possible to create mutants in vitro and then put it into a cell by transfection. A transient expression system will be used to analyze the cis-acting element in eukaryotes because it is not only fast but also free from the interference of chromatin structure. To make this strategy work, the wild type transcripts has to be either knocked out or distinguished from the mutant transcripts. Usually it is difficult to knock out the wild type gene in a cell. You can alternatively use a cell type which does not express the target gene; however, this method suffer from the criticism of having a different regulatory system in the cells you are using. By introducing a deletion or an insertion on the mutant gene, you can easily distinguish the wild type and mutant transcripts by S1 analysis. Several reporter system has been designed to monitor the transcription activity, such as the CAT, lacZ, or luciferase genes. You can simply make a chimeric gene by fusing a reporter gene right after the initiation site of the promoter you are interested in and then transfect this chimeric gene into the proper cell line.
Although you can assay the enzyme activity when you use a reporter system; however, it is preferrable to assay the steady state RNA concentration. Translation efficiency and protein stability may complicate the interpretation of transcription activity in the assay. Even though you quantify the RNA concentration, it is still not the perfect solution. RNA concentration is the net result of synthesis and degradation and the RNA synthesis is the net result of initiation, elongation, and termination. Thus, RNA concentration only relects the transcription initiation activity under the assumption that other factors are not changed among these mutants. Do you want to perform nuclear run-on experiment for all your mutants? You may not want to, because it is not cost-effectiveness. Some people use the CAT assay to get some clues and then analyze the RNA concentration for important mutants. You should make your own decision for your own approach.